Reverberation Mapping of Supermassive Black Holes using Machine Learning

Abstract

Accreting supermassive black holes at the centers of galaxies, known as active galactic nuclei (AGN), offer a unique window into the physics of accretion and feedback that shape galactic evolution. Yet, the small spatial scales of these regions remain inaccessible to direct imaging. Reverberation mapping circumvents this limitation by using time delays between correlated emission at different wavelengths to infer physical size scales. While X-ray reverberation probes the innermost accretion flow, continuum reverberation in the UV, optical, and infrared (UVOIR) traces reprocessing by the accretion disk and broad-line region (BLR). In this thesis, I develop and apply frequency-domain timing techniques based on Gaussian Process (GP) regression to study AGN reverberation across X-ray and UVOIR regimes. By modeling the empirical variability of AGN light curves with GPs, I interpolate onto an evenly sampled time grid, enabling robust estimation of Fourier-resolved time lags despite irregular sampling or large time gaps. I apply this method to NuSTAR observations of the Narrow-line Seyfert 1 galaxy Ark 564, introducing a multi-task GP model that jointly learns kernel hyperparameters across light curves. This enables the first simultaneous modeling of lag and flux spectra from both NuSTAR and XMM-Newton using a relativistic reverberation model to constrain black hole mass and disk properties. Recent reverberation campaigns with the Neil Gehrels Swift Observatory and ground-based telescopes have revealed significant discrepancies between observed inter-band lags and standard accretion disk theory. These include unexpectedly large lag amplitudes (the “accretion disk size problem”) and weak correlations between X-ray and UV/optical light curves. To investigate further, I analyze recent Swift campaigns of Mrk 335 and Mrk 817 using GP-based frequency-resolved lag analysis. In both sources, standard disk lags appear only on short timescales (high frequencies), while longer-than-expected lags dominate at low frequencies. These lag excesses are consistent with reprocessing at larger radii, similar to the BLR. Mrk 817 offers a rare opportunity to connect the inner and outer accretion flow: I detect the first simultaneous measurement of X-ray and UVOIR lags, effectively mapping the full disk. These lags vary significantly over the campaign, with longer delays during periods of stronger X-ray obscuration. This suggests that a disk wind may modulate the observed lags by introducing additional reprocessing and/or blocking ionizing flux from reaching more-distant material. To test this obscuration effect across a population, I conduct the first statistical study of UV/optical lag excess versus physical parameters across the Swift campaigns. The results show that the lag excess is driven entirely by obscured AGN, while the lags of unobscured sources are, on average, consistent with thin-disk theory. Regression analysis reveals that X-ray column density explains over 80% of the variance in lag excess. As for the X-ray/UV connection, obscured AGN also tend to show weaker correlations and more variable lags, suggesting that line-of-sight absorption not only contributes additional reprocessed emission that extends the UV/optical lags, but may also decouple or delay the X-ray and UV variability. To make GP-based time series analysis accessible to the community, I developed the STELA Toolkit, a fully documented Python package for computing frequency-domain data products using GPs. I also benchmark GP performance against other interpolation methods, including state-of-the-art transformers, paving the way for scalable, ML-enabled timing analysis in the era of time-domain surveys like Vera Rubin.